1. The number of all one to one functions defined from Set A = {1, 2, 3, 4} to itself is (A) 12 (B) 24 (C) 16 (D) 36?

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1. The number of all one to one functions defined from Set A = {1, 2, 3, 4} to itself is (A) 12 (B) 24 (C) 16 (D) 36?

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1. The number of all one to one functions defined from Set A = {1, 2, ...

Solution:

Concept: A function is said to be one to one or injective if no two elements of the domain A have the same image in the codomain B.

We have to find the number of all one to one functions defined from Set A = {1, 2, 3, 4} to itself.

Method:

We can solve this problem by using permutation and combination.

As all the elements of the domain have to be mapped to different elements in the codomain, the first element of the domain can be mapped to any of the 4 elements of the codomain.

After the first element is mapped, the second element can be mapped to any of the remaining 3 elements of the codomain. Similarly, the third element can be mapped to any of the remaining 2 elements and the last element can be mapped to the last remaining element.

Therefore, the total number of one to one functions is the product of the number of ways of mapping each element.

Hence, the number of one to one functions is given by:

Number of one to one functions = 4 × 3 × 2 × 1

Number of one to one functions = 24

Therefore, the correct answer is option (B) 24.

Answer: The number of all one to one functions defined from Set A = {1, 2, 3, 4} to itself is 24.

Community Answer

1. The number of all one to one functions defined from Set A = {1, 2, ...

Answer is B.Since the number of one-one functions from a set to itself is n! where n is the number of elements in the given set.In this case n=4,So 4! which is 24.

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1. The number of all one to one functions defined from Set A = {1, 2, 3, 4} to itself is (A) 12 (B) 24 (C) 16 (D) 36?

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